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Simplifying (4x + x2)(1 + -2x) = 0 Multiply (4x + x2) * (1 + -2x) (4x * (1 + -2x) + x2(1 + -2x)) = 0 ((1 * 4x + -2x * 4x) + x2(1 + -2x)) = 0 ((4x + -8x2) + x2(1 + -2x)) = 0 (4x + -8x2 + (1 * x2 + -2x * x2)) = 0 (4x + -8x2 + (1x2 + -2x3)) = 0 Combine like terms: -8x2 + 1x2 = -7x2 (4x + -7x2 + -2x3) = 0 Solving 4x + -7x2 + -2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -7x + -2x2) = 0 Factor a trinomial. x((1 + -2x)(4 + x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {0, 0.5, -4}
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